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the equation of the formulas in (27), whereas the normal interpretation is on the right side. The minimal witness set for monotone decreasing quantifiers is the empty set and because the empty set is the subset of any set, the left part of (27a) is a tautology, hence it is not equal to the right side, which is simply the meaning of the quantifier at most three horses (the set of sets which include at most three horses). In (27b), on the other hand, the part on the left side is equal to the one on the right side because the witness set of the weak quantifier three horses (the set of sets containing three horses) is identical to the meaning of the quantifier. (27) a. ∃P[P = ∅ ∧ P ⊆ Y] ≠ ∃X[|X| ≤ 3 ∧ X = ⟦horse⟧ ∩ Y] b. ∃P[P ⊆ ⟦horse⟧ ∧ |P|=3 ∧ P ⊆ Y] = ∃X[|X| = 3 ∧ X ⊆ ⟦horse⟧ ∩ Y] The topicality condition draws a line between topicable and non-topicable quantifiers. With some simplification, weak quantifiers, indefinites, and the universal all-quantifier are topicable, whereas monotone decreasing quantifiers, non-monotone quantifiers, the universal quantifier every, and monotone increasing quantifiers are non-topicable. This is close (though not identical) to what we saw for the Albanian clitic doubling patterns. An exception are monotone increasing quantifiers which may be clitic doubled in Albanian, even though according to the topicality condition they are non-topicable. But as Endriss (2009) herself acknowledges, matters are not so simple and straightforward, since even a monotone increasing determiner such as the English several allows for a topical wide scope reading and non-exhaustive interpretation, as shown in (28) (from Endriss 2009, her example 6.44). (28) a. Several mathematicians were at the party yesterday. They danced all night. b. The other mathematicians at the party only drank a lot. The non-exhaustive interpretation of the quantifier several mathematicians shows that it can be interpreted as a vague bare numeral weak quantifier similar to n. Under such an interpretation, it can then meet the topicality condition. To conclude this section, let us summarize our reasoning so far: if we put aside the information structure effects, the set of quantifiers which can be clitic doubled in Albanian consists of weak quantifiers (bare numeral and monotone increasing quantifiers) and strong quantifiers. Bare numerals and the all strong quantifier are uncontroversially argued to be good candidates to be topics by Endriss (2009). As for monotone increasing quantifiers, they allow for a topical interpretation under a non-exhaustive interpretation. Further scrutiny notwithstanding, we assume that the same process of reinterpretation is responsible for the acceptability of monotone increasing clitic doubled quantifiers in Albanian. The next section is dedicated to those strong quantifiers which allow clitic doubling in Albanian but their status as topics (in a theory like Endriss’) is at least controversial. 3.2. Presuppositional determiners As was pointed out in §2.1, all DPs headed by strong determiners may be clitic doubled in Albanian. The fact that the DPs headed by the strong determiners çdo ‘every’, secilin ‘each’, të shumtët ‘most’, and asnjërin ‘neither (one of)’/‘none (of)’ may be clitic doubled in Albanian – see the examples in (29) – is problematic for our attempt to explain the Albanian clitic doubling purely algebraically, because singular universal quantifiers are assumed to be non-topicable in Endriss’ (2009) analysis, as was demonstrated by the ungrammaticality of (20b). 122
(29) a. (E) lexova çdo libër. CL.ACC.3S read.1s every book ‘I read each book.’ b.(E) lexova secilin libër. CL.ACC.3S read.1s each.the ACC book ‘I read each book.’ c. (I) lexova më të shumtët (e librave). them Cl.ACC read.1s sup most.pl.the agr books.the ACC ‘I read most (books).’ d.Nuk (e) lexova asnjërin (libër) / (prej librave). not CL.ACC.3S read.1s neither.the ACC book / from books.the DAT ‘I read neither (book / of the books).’ However, the fact that the DPs headed by these strong determiners may be clitic doubled is not necessarily an argument against Endriss’ 2009 framework because the minimal witness set for the universal quantifiers is the same for singular and plural; the minimal witness set for the quantifiers every book, all books and each book in any model would be the same, namely the set of all the books in the universe of discourse. Other things being equal, we would then expect universal quantifiers to be good topics independently of their grammatical number, with the consequence that the English facts in (20b) are surprising. Indeed Endriss 2009 attributes the non-topicability of singular universal quantifiers to a clash between the denotation of the minimal witness set and the morphological number of the quantifier (and the morphological number of the resumptive pronoun in the case of left-dislocated noun phrases like in (20b)). According to her, because the minimal witness set denotes plurality and the grammatical number on the quantifier (and the resumptive pronoun) is singular, there arises a mismatch, which is the reason for the ungrammaticality of singular universal quantifiers in syntactic positions associated with topics. It could be hypothesized that, for some reason, this clash in number doesn’t arise in Albanian, hence the singular universal quantifiers are topicable in this language, perhaps due to the fact that clitics are very light elements (although they are not underspecified for number in Albanian). We would need to examine this hypothesis more thoroughly, but for now suffice it to mention that, as is well-known, a simple mapping between singular grammatical number and non-plurality of its denotation isn’t always viable. For instance, collective nouns like team or government in English denote pluralities but are grammatically singular (even though they may determine plural agreement). Similarly, from a cross-linguistic perspective, Slavic languages exhibit singular verbal agreement with subject DPs headed by numerals higher then four. Another problematic case is the determiner asnjërin ‘neither (one of the)’/‘none (of the)’. As the determiner is negative strong, its minimal witness set is simply the empty set. Being so, we would expect that clitic doubling of a DP headed by this determiner shouldn’t be possible, contrary to fact – see (29d). We assume that the reason for this is the presuppositional behavior of determiners like neither. In this respect, there is a common core for all four quantifiers discussed in the present section: all these determiners are presuppositional, i.e., they presuppose the non-emptiness of the set denoted by their noun argument. We cannot go into the details of the presuppositional treatment of quantifiers here but would nonetheless like to mention that there is an ongoing discussion between the presuppositional and non-presuppositional treatment of quantifiers, which as far as we know has not been resolved yet. But starting at least with Barwise & Cooper (1981), it is usual to treat the determiners the, both, and neither as presuppositional. Nevertheless other determiners such as every, all, and most are also sometimes considered presuppositional, so basically all strong determiners are argued to 123
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